On the oxide thickness estimation from the current-voltage characteristics of thin metal-oxide-semiconductor structure

Based on the solution of the time-dependent Schrodinger equation within the framework of the effective mass theory, a complete quantum mechanical electron tunneling through a biased square potential model with abrupt interfaces was deduced. Barriers of 3 eV height and width: 50, 70, 100 and 140 , were investigated. Current density-voltage (J-V) curves were computed for Al/SiO₂/n⁺Si structure. The computed J-V curves exhibited oscillations at applied voltages above 3 V. For oxide thickness estimation, the position of the oscillation extrema from this quantum mechanical model were fitted to a wave interference formula and showed excellent agreement for oxide layer widths less than 50 A. However, a systematic deviation appeared for layers larger than 50 A. We show that for accurate oxide thickness estimation the electron effective mass on layers other than the oxide layer and the electron energy distribution are to be included in modeling.